It is not read only, you should be able to upload files to those cloud storage providers via the File Storage area. If you want to include those files in outgoing emails you can use the ...>Link File functionality in the compose window to include an attachment of your choosing. 

You can preview attachments via our file storage integrations but I don't see an option to save directly to cloud storage from a message attachment. It would be pretty neat if you could save attachments in messages directly to cloud storage though! Is that what you were hoping for here?

Strange, I can't get it on Dropbox and Onedrive, upload is disabled

Currently, only the OwnCloud integration supports uploading to a cloud storage provider. We do have a feature request in our backlog to implement this capability for other cloud storage integrations.